Grade Level: 9-12 Topic: Fractions and Compounding Probability
Objectives:
Student will understand that fractions are used to find probabilities.
Student will know the term event, set, element, combination, probability, independant and compound. Students will also know the formula of probability (events wanted/total events).
Student will be able to show how to find and use probabilities.
Maine Learning Results Alignment
Maine Learning Result: Mathematics - B. Data
Probability
Grade 9 - Diploma
5. Students understand the relationship of probability to relative frequency and know how to find the probability of compound events.
b. Find expected value of events
Rationale: This lesson meets the Maine Learning Results because students will be able to calculate simple probabilities and use them to make predictions by compounding independent sets of data.
Assessment
Formative (Assessment for Learning) Students will work together in groups to gather the data collected from the student survey and find simple probabilities using these facts. Students in each group will be problem solving and working together to answer certain combinations of physical characteristics. Students will also participate in guided practice half way through the lesson.
Summative (Assessment of Learning) Each student will create a comic representation of their predicted "new student" whom they have already created during class. They will have a week to finish this product (outside of class) and will use Comic Life to create their ending product. These will be graded using a checklist and will count towards the individual student's overall homework grade.
Integration
Technology: A Sportscenter commercial (http://youtube.com/watch?v=0HxRkFtIIdA) portraying a "New"s Anchor to the show to use as the hook of introducing the main theme and concept of the lesson. Students will also use Comic Life to create a comic representation characterizing the "new student" they have calculated the probability of.
Science: Students will be analyzing physical characteristics of themselves and each other (eye color, hair color, left/right handed, glasses/contact or neither).
English: Students will have to incorporate a mathematics driven dialog explaining the probabilities behind their "new student's" characteristics as part of using Comic Life.
Art: Students will design a short comic strip using Comic Life to represent their "new student" and convey their understanding of calculating probability.
Groupings
After lecture, we will discuss as a class what it is like to be the "new kid" in the class. The class will already be in their group of 4. Groups will be made by pulling slips of paper out of a box upon entering class. As a group they will represent one of the four physical characteristics picked from the box. Each group will fill out the graphic organizer (survey) over physical characteristics (i.e. hair color, eye color, right/left handed. glasses/contacts or neither). Then each member gathers their physical characteristic data from their group and relay it to the rest of the class as the teacher compiles all the numbers on the board. As a class we will compute the "class probabilities" for physical characteristics then each group will be assigned a certain combination of traits for a new student and compound the probability of a "new student" to have those characteristics. Then each student will pick four traits in whic they think a new student could have.
Differentiated Instruction
Strategies Mathematical Reasoning: Students will have to calculate simple probabilities and draw predictions from them. Interpersonal: Students will be working in groups of 4. Verbal: Students will write a dialog for a comic strip, describing their predicted new student. Spatial/Visual: Students will take notes that have been written on the white board as well as watch the hook (http://youtube.com/watch?v=0HxRkFtIIdA). Naturalist: Students will be analyzing physical traits of other classmates. Intrapersonal: Students will be analyzing their own physical traits and working on their own to create the final product.
Modifications/Accommodations
I will review students' IEPs, 504s ELLIDEPs and make the appropriate modifications and accommodations for students. All subject matter will be appropriate for everyone, the only forseeable issue may arise for students with colorblindness and if that is the case those students will be able to get aid from another classmate or instructor to differentiate colors.
Absent Students: If a student is absent for class, they must have an excused absence (filed with the school) in order to get a chance to earn back their points from missing class. Students will be responsible for making up the activity they missed in class. Absent students are encouraged to see a peer, instructor or consult the class wiki to gather any information they need from this class. Students with excused absences must do the assignment on their own or work with another student who was out for this class (to gain the group aspect of class). By doing the work and putting forth an effort students with excused absences can earn back the participation points (20) which they would have received for the class. Students who do not have excused absences will not be able to earn back the participation points for this class (20) but they are still eligible to do the assignment on their own since the assignment will be their first quiz grade
Extensions
As a class we will use the Sportscenter commericial ( http://youtube.com/watch?v=0HxRkFtIIdA) as a Type II technology to get the students actively thinking about what a new student would look like if they were to join our class today. This will allow students to be thinking about a "new student" and will give them a visual, from the real world, which we will be applying the concepts of probability to. Students will also use Comic Life as a Type II technology to create a visual and dialog of their "new student" allowing them to not just find probabilities but make the math come to life by applying it and seeing a finished product.
Materials, Resources and Technology
Syllabus
Laptops
Projector
Comic Life Software
Checklist for Comic Life Assignment
Guided Practice Worksheet
Chalk/Marker Board
Maine Standards for Initial Teacher Certification and Rationale
Standard 3 - Demonstrates a knowledge of the diverse ways in which students learn and develop by providing learning opportunities that support their intellectual, physical, emotional, social, and cultural development. Rationale:This lesson addresses the Maine Standards for Initial Teacher Certificate by allows students multiple opportunities to gather, relate and understand the content of the lesson. Students will be able to relate their own experiences with being a new student to a class or remembering a class where a new student entered in the middle of the school year. By being able to relate probability to the experience of being or seeing a new student will ultimately give the content a direct application to the real world. The comic representation for each students"new student" will allow them to create a physical representation of the mathematics used to define the "new student". Students will also work together in small groups and offer feedback to one another to gain an understanding of the material and explore the different aspects to it.
Standard 4 - Plans instruction based upon knowledge of subject matter, students, curriculum goals, and learning and development theory. Rationale:This lesson addresses the Maine Standards for Initial Teacher Certificate by gaging where students are with the material by asking students about prior knowledge to see where the instructor needs to start with explaining the concepts of probability. Students will be able to self-assess their understanding and knowledge through group work and discussions analyzing how they are using concepts of probability and why. In addition MI theory will be integrated into the lesson to create an optimal learning atmosphere (see Strategies). Lastly students with IEP's, 504's or ELLIDEP's will be reviewed and appropriate modifications to the lesson plan will be made.
Standard 5 - Understands and uses a variety of instructional strategies and appropriate technology to meet students’ needs. Rationale:This lesson addresses the Maine Standards for Initial Teacher Certificate by letting the students take part in multiple activities using various technologies. Students will be viewing a video commercial ([[http://youtube.com/watch?v=0HxRkFtIIdA%29%7Chttp://youtube.com/watch?v=0HxRkFtIIdA%29%3C/span%3E%3Cspan|http://youtube.com/watch?v=0HxRkFtIIdA%29|http://youtube.com/watch?v=0HxRkFtIIdA)<span]] at the start of class as a hook. Students will also use the software Comic Life to create a visual corresponding with the data of physical characteristics they calculated probabilities with respect to, to analyze a possible new student. Students will be working together in groups to explore probability and how it works and functions as well as learning it through a lesson and note taking portion of class.
Standard 8 - Understands and uses a variety of formal and informal assessment strategies to evaluate and support the development of the learner. Rationale:This lesson addresses the Maine Standards for Initial Teacher Certificate by offering students multiple forms of assessments through out the class. Students will be given guided practice problemst to see where they are currently with the material. From there students will be working together and forming conclusions and questions about probability to be discussed as a class. This portion of the class will allow students to get feedback on their thought process behind their problem solving of examples to make corrections and revisions as they develop towards their final product. The students use Comic Life to make a visual representation of their "new student" in which they created using fractions and compounding probabilities. Students will have as much as a week to complete the final version of their Comic Life representation.
Teaching and Learning Sequence:
(0-15 minutes) The students will come into the room and the desks will be in rows all facing the board and they will be in five clusters of four desks each group. The students will take their seats and find the agenda of the class written on the left side of the board. It would read,
Class Agenda
Welcome (0-15)
a. “Applying Probability to Life” Syllabus
b. What will we learn today?
c. “New”s Anchor
Lecture (15-35)
Vocabulary
Fractions with Probability
Examples
Guided Practice (35-45)
“New Classmate Activity”(45-70)
Survey
Probability
Your turn to try
Comic Life Interpretation
Wrap-Up (70-80)
What did we learn today?
What will we learn tomorrow?
How will today connect to tomorrow?
The following directions would be on the whiteboard in big bold letters “Everyone needs to pick a slip of paper out of the box and find three other classmates with all different labels on their slip of paper, and sit together as a group.” There will be 20 slips of paper (or number of students in the room) with an equal number labeled hair color, right hand/left hand, eye color, and contacts/glasses. Once all of the students have found their seats the students will hear from the teacher that they will be starting a new unit called “Applying Probability to Life” and a syllabus will be passed around. Students will go over syllabus as a class and ask any questions they may have. After that the teacher will inform the students what they will be learning about. The teacher will discuss the topic of probability, what it is and how we can apply it to our surroundings and give a brief overview to the “New Student Activity” that will be done in class and its relevance to the lesson. Lastly before the lecture is to start the students will view a commercial entitled “New”s Anchor”. Where, What, Why, Hook. Tailor:Spatial, Verbal, Auditory
(15-45 minutes) Next the teacher will begin the lecture by putting up all of the vocabulary with examples of each term (See attached notes). Students will be required to take notes, they should be encouraged to ask questions and can request extra examples if needed. The students will then learn about fractions and how they can be used to calculate probabilities (this should be tie directly back to the vocabulary learned). To conclude the lecture the students will see 4 examples done on the board calculating probabilities, two examples will include compounding independent sets. To transition out of lecture time, the students will attempt 2 problems on their own as a form of guided practice. The teacher will ask the class to be very quiet and work independently on the two examples written on the board. Whiel the teacher will be walking around the room and students will be able to ask the teacher questions at any time. Students will have five to ten minutes to work on the problems.Equip, Tailor: Spatial, Visual, Auditory
(45-70 minutes) After the students pass in their guided practice examples, they will pick up a data table to fill out to start the “New Classmate Activity”. As a class the teacher will have the students record the data of their own table. The data will consist of tracking each of the four physical characteristics from the box at the beginning of class. Each student in the group will be in charge of recording their specific characteristic. If a student drew hair color they would survey their group about hair color and record the data. Then as a class the teacher will ask each student to relay their data to the rest of the class and the teacher will compile it all on the white board for the whole class to copy down in their data tables. As a class compute all the probabilities for having each physical characteristic. Now pass out slips of paper that have four different combinations of eye color, hair color, right/left hand preference, contacts/glasses or neither in which a “new student” to our class might have. Each group will work on solving for the probabilities for all four examples and each student is required write down all examples. During this time the age appropriate music will be played in the classroom until the end of group work time is over. Once the students have been able to try the problems and ask the teacher any questions they will be given their Comic Life Assignment. Students will be asked to pick one of each of the four physical characteristics described in class to use to describe the “a new student” to the class. In this Comic Life interpretation of the new student there should be a dialog describing how the student arrived at the probability of the “new student” having thos characteristics, based on the probabilities from class. The students will be given a week to complete this and it will count as a quiz grade covering calculating and compounding simple probabilities. If students would wish to pick more than just the four physical characteristics they can, they must just define what the probability would be of that characteristic. Explore, Re-think, Revise, Tailor: Intrapersonal, Interpersonal, Verbal, Mathematical/Logical, Musical, Naturalist
(70-80 minutes) To wrap up the class the teacher will recap the material learned in class by reviewing the class agenda still located on the board. The students will be able to ask any last questions about the material or their assignment. The topic of next class will be introduced as applying what they learned about today. They will be using probability to find out if it gives facts or ideas about sets of data. Students will be expected to review the vocabulary from this lesson to be ready for next class. Evaluate, Tailor:Intrapersonal, Mathematical/Logical, Visual/Spatial.
UMF LESSON PLAN FORMAT
Teacher’s Name: Mr. Nick Hart Lesson # : One
Grade Level: 9-12 Topic: Fractions and Compounding Probability
Objectives:
Maine Learning Results Alignment
Probability
Grade 9 - Diploma
5. Students understand the relationship of probability to relative frequency and know how to find the probability of compound events.
b. Find expected value of events
Rationale: This lesson meets the Maine Learning Results because students will be able to calculate simple probabilities and use them to make predictions by compounding independent sets of data.
Assessment
Students will work together in groups to gather the data collected from the student survey and find simple probabilities using these facts. Students in each group will be problem solving and working together to answer certain combinations of physical characteristics. Students will also participate in guided practice half way through the lesson.
Each student will create a comic representation of their predicted "new student" whom they have already created during class. They will have a week to finish this product (outside of class) and will use Comic Life to create their ending product. These will be graded using a checklist and will count towards the individual student's overall homework grade.
Integration
Science: Students will be analyzing physical characteristics of themselves and each other (eye color, hair color, left/right handed, glasses/contact or neither).
English: Students will have to incorporate a mathematics driven dialog explaining the probabilities behind their "new student's" characteristics as part of using Comic Life.
Art: Students will design a short comic strip using Comic Life to represent their "new student" and convey their understanding of calculating probability.
Groupings
Differentiated Instruction
Mathematical Reasoning: Students will have to calculate simple probabilities and draw predictions from them.
Interpersonal: Students will be working in groups of 4.
Verbal: Students will write a dialog for a comic strip, describing their predicted new student.
Spatial/Visual: Students will take notes that have been written on the white board as well as watch the hook (http://youtube.com/watch?v=0HxRkFtIIdA).
Naturalist: Students will be analyzing physical traits of other classmates.
Intrapersonal: Students will be analyzing their own physical traits and working on their own to create the final product.
I will review students' IEPs, 504s ELLIDEPs and make the appropriate modifications and accommodations for students. All subject matter will be appropriate for everyone, the only forseeable issue may arise for students with colorblindness and if that is the case those students will be able to get aid from another classmate or instructor to differentiate colors.
Absent Students:
If a student is absent for class, they must have an excused absence (filed with the school) in order to get a chance to earn back their points from missing class. Students will be responsible for making up the activity they missed in class. Absent students are encouraged to see a peer, instructor or consult the class wiki to gather any information they need from this class. Students with excused absences must do the assignment on their own or work with another student who was out for this class (to gain the group aspect of class). By doing the work and putting forth an effort students with excused absences can earn back the participation points (20) which they would have received for the class. Students who do not have excused absences will not be able to earn back the participation points for this class (20) but they are still eligible to do the assignment on their own since the assignment will be their first quiz grade
As a class we will use the Sportscenter commericial ( http://youtube.com/watch?v=0HxRkFtIIdA) as a Type II technology to get the students actively thinking about what a new student would look like if they were to join our class today. This will allow students to be thinking about a "new student" and will give them a visual, from the real world, which we will be applying the concepts of probability to. Students will also use Comic Life as a Type II technology to create a visual and dialog of their "new student" allowing them to not just find probabilities but make the math come to life by applying it and seeing a finished product.
Materials, Resources and Technology
Laptops
Projector
Comic Life Software
Checklist for Comic Life Assignment
Guided Practice Worksheet
Chalk/Marker Board
Source for Lesson Plan and Research
http://youtube.com/watch?v=0HxRkFtIIdA
Maine Standards for Initial Teacher Certification and Rationale
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certificate by allows students multiple opportunities to gather, relate and understand the content of the lesson. Students will be able to relate their own experiences with being a new student to a class or remembering a class where a new student entered in the middle of the school year. By being able to relate probability to the experience of being or seeing a new student will ultimately give the content a direct application to the real world. The comic representation for each students"new student" will allow them to create a physical representation of the mathematics used to define the "new student". Students will also work together in small groups and offer feedback to one another to gain an understanding of the material and explore the different aspects to it.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certificate by gaging where students are with the material by asking students about prior knowledge to see where the instructor needs to start with explaining the concepts of probability. Students will be able to self-assess their understanding and knowledge through group work and discussions analyzing how they are using concepts of probability and why. In addition MI theory will be integrated into the lesson to create an optimal learning atmosphere (see Strategies). Lastly students with IEP's, 504's or ELLIDEP's will be reviewed and appropriate modifications to the lesson plan will be made.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certificate by letting the students take part in multiple activities using various technologies. Students will be viewing a video commercial ([[http://youtube.com/watch?v=0HxRkFtIIdA%29%7Chttp://youtube.com/watch?v=0HxRkFtIIdA%29%3C/span%3E%3Cspan|http://youtube.com/watch?v=0HxRkFtIIdA%29|http://youtube.com/watch?v=0HxRkFtIIdA)<span]] at the start of class as a hook. Students will also use the software Comic Life to create a visual corresponding with the data of physical characteristics they calculated probabilities with respect to, to analyze a possible new student. Students will be working together in groups to explore probability and how it works and functions as well as learning it through a lesson and note taking portion of class.
Rationale: This lesson addresses the Maine Standards for Initial Teacher Certificate by offering students multiple forms of assessments through out the class. Students will be given guided practice problemst to see where they are currently with the material. From there students will be working together and forming conclusions and questions about probability to be discussed as a class. This portion of the class will allow students to get feedback on their thought process behind their problem solving of examples to make corrections and revisions as they develop towards their final product. The students use Comic Life to make a visual representation of their "new student" in which they created using fractions and compounding probabilities. Students will have as much as a week to complete the final version of their Comic Life representation.
Teaching and Learning Sequence:
Class Agenda
Welcome (0-15)
a. “Applying Probability to Life” Syllabus
b. What will we learn today?
c. “New”s Anchor
Lecture (15-35)
- Vocabulary
- Fractions with Probability
- Examples
Guided Practice (35-45)“New Classmate Activity”(45-70)
- Survey
- Probability
- Your turn to try
- Comic Life Interpretation
Wrap-Up (70-80)- What did we learn today?
- What will we learn tomorrow?
- How will today connect to tomorrow?
The following directions would be on the whiteboard in big bold letters “Everyone needs to pick a slip of paper out of the box and find three other classmates with all different labels on their slip of paper, and sit together as a group.” There will be 20 slips of paper (or number of students in the room) with an equal number labeled hair color, right hand/left hand, eye color, and contacts/glasses. Once all of the students have found their seats the students will hear from the teacher that they will be starting a new unit called “Applying Probability to Life” and a syllabus will be passed around. Students will go over syllabus as a class and ask any questions they may have. After that the teacher will inform the students what they will be learning about. The teacher will discuss the topic of probability, what it is and how we can apply it to our surroundings and give a brief overview to the “New Student Activity” that will be done in class and its relevance to the lesson. Lastly before the lecture is to start the students will view a commercial entitled “New”s Anchor”. Where, What, Why, Hook. Tailor:Spatial, Verbal, AuditoryExplore, Re-think, Revise, Tailor: Intrapersonal, Interpersonal, Verbal, Mathematical/Logical, Musical, Naturalist
Evaluate, Tailor: Intrapersonal, Mathematical/Logical, Visual/Spatial.